Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×C5×#126 ⋊ C2 |
| Hall | C3×C5 ⋊ #563 |
| Sylow | C5 ⋊ #5712 |
| Sylow | C3 ⋊ #66046 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D15 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Fitting | C3×C5×#126 | C2 |
| prime radical | C2×#1220 | C22 |
| hypercenter | #126 | D15 |
| hypocenter | C3×C5 | #563 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ #126 | |
392 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^6,3,5|b^2=f,d^2=e,c^a=cf,d^a=def,g^a=g^2,h^a=h^4,c^b=ce,d^b=df,d^c=df117 conjugacy classes — view the full character table.
| maximal subgroup of | D15×#563, C2×#11756471, D5×#5712, … |
| maximal normal subgroup of | D15×#563, C2×#11756471, D5×#5712, … |
| maximal quotient of | #14330688, #14330700, #14330978, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10666);